A family with three young children just moved into a house with a yard that is not fenced in. The previous owner gave them 256 feet of fencing to enclose part of their backyard against the house (see image). The quadratic function A
(
x
)
=
x
(
256
−
2
x
)
gives the area,
A
, when
x
is the width used. Find the width that gives the maximum area, and then find the maximum area that can be enclosed.